One of the legs of a right-angled triangle is 4 cm, the other 3 cm. From the top of the right angle, a perpendicular is dropped to the hypotenuse. Find its length.
1. Vertices of the rectangle A, B, C. ∠C = 90 °. BC = 4 cm. AC = 3 cm. CH – perpendicular to the hypotenuse.
2. We calculate the length of the hypotenuse AB using the Pythagorean theorem:
AB = √BC² + AC² = √4² + 3² = √16 + 9 = √25 = 5 cm.
3. Calculate the area (S) of a given triangle:
S = BC x AC / 2 = 4 x 3/2 = 6 cm².
4. Calculate the length of the perpendicular CH using another formula for calculating the area (S) of a given triangle:
S = AB x CH / 2.
CH = 2S / AB = 6 x 2/5 = 2.4 cm.
Answer: the length of the perpendicular CH is 2.4 cm.
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